Generating function
$$U_{1068}(x, y) = \frac{\left(1 - \sqrt{1 - 4 x}\right)^{3} \left(1 - \sqrt{1 - 4 y}\right)}{16 x^{3} y}$$
Explicit formula
$$T_{1068}(n, m, k) = \frac{3 k^{2} {\binom{k + 2 m - 1}{m}} {\binom{3 k + 2 n - 1}{n}}}{\left(k + m\right) \left(3 k + n\right)}$$
Data table
1 1 2 5 14 42 132
3 3 6 15 42 126 396
9 9 18 45 126 378 1188
28 28 56 14 392 1176 3696
9 9 18 45 126 378 1188
297 297 594 1485 4158 12474 39204
1001 1001 2002 5005 14014 42042 132132
Export
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